Expert: Vishwas K Hajirnis - 7/20/2004

Question
If theta is an angle in standard position and its terminal side passes through the point
(-1/2,-sqrt(3)/2) on the unit circle, then a possible value for theta is
(1)60degrees
(2)120degrees
(3)240degrees
(4)300degrees
The answer is 240degrees, but can't get it.Please help.Thank you.

Answer
Without doing detailed calculations we can say that
the answer is 240 degrees.
Since the point is on the unit circle its x-co ordinate
must be cos(theta) and y-co ordinate must be sin(theta).
Since both sin(theta) and cos(theta) are negative we
know the point must be in the third quadrant. And amongst
the answers given here only (3) 240 degrees is in the
third quadrant, hence it must be the answer.